Theorems · Theorem · real analysis
edist_naturalParameterization_eq_zero
∀ {α : Type u_1} [inst : LinearOrder α] {E : Type u_2} [inst_1 : PseudoEMetricSpace E] {f : α → E} {s : Set α},
LocallyBoundedVariationOn f s →
∀ {a : α}, a ∈ s → ∀ {b : α}, b ∈ s → edist (naturalParameterization f s a (variationOnFromTo f s a b)) (f b) = 0- Defined in
- Mathlib.Analysis.ConstantSpeed
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- ENNRealstatement · cited by 9,879
- LinearOrderstatement and proof · cited by 8,572
- PseudoEMetricSpacestatement and proof · cited by 1,536
- EDist.ediststatement · cited by 735
- LocallyBoundedVariationOnstatement and proof · cited by 41
- Function.invFunOnproof · cited by 35
- variationOnFromTostatement and proof · cited by 33
- Function.invFunOn_posproof · cited by 3
- naturalParameterizationstatement · cited by 2
- variationOnFromTo.edist_zero_of_eq_zeroproof · cited by 1
- variationOnFromTo.eq_left_iffproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- has_unit_speed_naturalParameterizationproof · cited by 0